Technical Field
The present description relates to beamforming based on a plurality of microphones arranged in an array or arrays with respect to a reference point, including acquiring microphone signals issued by said plurality of microphones, which may be preferably applied to sound source localization.
Description of the Related Art
It is very well known to use arrays of microphones to perform sound, or acoustic, source localization, i.e., locating a sound source given measurements of the sound field, which in particular are obtained by such microphones.
It is also known to use signal processing modules such as DSP (Digital Signal Processing) modules to process the signals from each of the individual microphone array elements to create one or more Virtual Microphones (VMIC).
Virtual Microphones (VMIC) are therefore a combination of filtered versions of the signals sensed by an array of microphones arranged in a particular spatial geometry.
Virtual Microphones may be obtained in a recursive fashion using combinations of other Virtual Microphones organized in virtual arrays. Therefore, in general, a Virtual Microphone is characterized by a hierarchical virtual structure with a number L greater equal than one of layers: the first layer combines physical microphone signals generating an array of Virtual Microphones and any higher layer combines Virtual Microphone signals forming further arrays of Virtual Microphones.
For what concerns the Virtual Microphone position, considering an array of virtual or physical microphones, the array is geometrically described with respect to a fixed reference point in the physical space: the Virtual Microphone resulting from the combination of microphone signals of this array is virtually positioned in the same fixed reference point of the array.
For what regards a general polar pattern function, a Virtual Microphone is characterized by an omnidirectional or directive polar pattern or directivity pattern.
An N-th order frequency-independent microphone directivity pattern Γ(θ) is defined as:Γ(θ)=a0+a1 cos(θ)+a2 cos2(θ)+ . . . +aN cosN(θ)θ being the polar angle, 0<θ≦2π, and a0, . . . , aN coefficients of the pattern.
It is convenient to set such coefficients as follows:a0=1−a1−a2− . . . −aN so that it is obtained a directivity pattern:
      Γ    ⁡          (      θ      )        =      1    -                  ∑                  I          =          1                N            ⁢              a        i              +                  ∑                  I          =          1                N            ⁢                        a          i                ⁢                              cos            i                    ⁡                      (            θ            )                              
In the following a Virtual Microphone characterized by a polar pattern of the N-th order will be referred to as an N-th order Virtual Microphone.
Directive Virtual Microphones are known. Known DSP techniques allow building directive Virtual Microphones of any order starting from arrays of (physical) omnidirectional microphones. Two broad classes of such DSP techniques are known as:
filter and sum techniques;
Differential Microphone Array techniques.
Differential Microphone Arrays (DMAs) are built by subtracting from each other the delayed microphone signals of the array.
The delays can be tuned in order to obtain a Virtual Microphone with the desired polar pattern shape, according to well known design principles.
The two broadest classes of DMAs with uniform geometries are:                Uniform Linear Arrays (ULA); and        Uniform Circular Arrays (UCA).        
Also Linear DMAs with non-uniform geometries have been discussed.
In a First Order Differential ULA, shown schematically in FIG. 1, an array 11 is constituted of two physical omni-directional microphones M1, M2, supplying a pair of microphone signals (m−d/2, md/2), positioned at a distance d one with respect to the other. A reference point O of the array is placed at the origin of the z-y Cartesian diagram. A sound wave of pressure amplitude P0 and frequency ω propagates along a propagation vector kin direction of such array. With θ is indicated the direction angle, i.e., the angle between the propagation vector k and the horizontal axis z of the array of microphones. The pair of microphone signals (m−d/2, m+d/2) is subtracted in a subtraction node 13, after applying to one of the two signals in a delay module 12 a delay τ. Varying τ the designer can adjust the resulting polar pattern shape.
The delay module 12 and subtraction node 13 identify a Virtual microphone 15 structure, having as input the pair of microphone signals (m−d/2, m+d/2) and as output a first order Virtual Microphone is obtained generating a virtual Microphone signal V(t), in particular here the resulting first order Virtual Microphone signal V1(t) is expressed as:V1(t)=m+d/2(t−τ)−m−d/2(t)
A filter 14, Hc(ω), is provided at the output of the virtual microphone structure 15 to operate on the Virtual Microphone signal V1(t), which is a correction filter (i.e., low pass filter), applied to the Virtual Microphone V1(t) signal in order to compensate for the frequency dependent effect of the signal subtraction.
The distance d between the microphones of the array 11 must be small enough with respect to the wavelength of the signal so that it can be considered negligible.
The shape of the polar pattern will be almost constant over a broad range of frequencies.
The polar pattern coefficient a1 is related to the delay τ by the formula:
  τ  =                              a          1                -        1                    a        1              ⁢          d              c        s            where cs is the speed of sound.
In FIG. 2 it is shown a structure producing as a result a second order Virtual Microphone. As it can be seen the structure of FIG. 1 of first order Virtual Microphone with a pair of microphones, which signals are sent to a difference module, is replicated. Three microphones M1, M2, M3 define two pairs of microphones at level L1 with two first order Virtual Microphones 151, including a delay and a difference module, like in FIG. 1, while at level L2 another corresponding Virtual Microphones 152, collects the output of such first order Virtual Microphones 151 operating the same delay and difference operations, although the delay value can be different. The chain is concluded, like in FIG. 1, by the filter 14. As mentioned, a first delay τ1, associated to the delay module of level L1, and a second delay τ2, associated to the delay module of level L2, can be tuned by the designer in order to obtain a Virtual Microphone with arbitrary directive polar pattern of the second order
Setting the polar pattern coefficients a1=η1+η2−2η1η2 and a2=η1η2 it is obtained for the delays:
      τ    1    =                    (                              η            1                    -          1                )                    η        1              *          d              c        s            and
      τ    2    =                    (                              η            2                    -          1                )                    η        2              *          d              c        s            
In FIG. 3 it is shown a third order Virtual Microphone structure 153, from an array of microphones 11 including four microphones M1, M2, M3, M4 which is characterized by a three levels L1, L2, L3 hierarchical virtual structure.
With reference to FIG. 4, it is possible to derive N-th order Virtual Microphones also with the alternative recently developed class of Differential Uniform Circular Arrays (UCA). UCAS are characterized by the spatial geometry depicted in FIG. 4, where the microphones, M1, M2 . . . Mm . . . MM, with M being the number of microphones, are uniformly displaced on a circumference at positions identified by angles ψm, defining an array 21. In particular, in FIG. 4 with ψm is indicated the angle corresponding to the generic m-th microphone Mm. For deeper understanding of UCAs it is here made reference to the book “Design of Circular Differential Microphone Arrays”, Benesty, Jacob, Jingdong, Chen, Cohen, Israel, Springer Verlag, 2015.
It is here underlined the fact that, indicating with N the number of Virtual Microphones obtained by M physical microphones, the maximum polar pattern order obtainable with an UCA is Nmax=M/2, which means that with M=2 or M=3 microphones it can be derived up to a first order Virtual Microphone; with M=4 or M=5 microphones it can be derived up to a second order Virtual Microphone; with M=6 or M=7 microphones it can be derived up to a thirst order Virtual Microphone; and so on. The higher the number M of microphones, the more robust is the DMA array. It is possible doing steering in all the M directions identified by the angle ψm.
Virtual Microphone polar patterns have always a symmetric shape with respect to the z axis. If it is desired only one main lobe in the directivity pattern, for ULA arrays it must aim at 0 degrees or at 180 degrees only.
Also polar patterns of Virtual Microphones obtained using differential UCA arrays are symmetric with respect to an axis, since a symmetry constraint is always applied in the derivation.
The symmetry axis may be any of the M straight lines joining the center of the array and the M microphones. In general it is not possible to design the Virtual Microphone polar pattern with the main lobe aiming at a direction different from angle ψm at which each of the M microphones is set, with 1≦m≦M. As explained in the above mentioned publication by Benesty et al., applying super-directive beamforming to UCA and getting rid of the symmetry constraint it is possible to design Virtual Microphones aiming at arbitrary directions, but the shape of the resulting polar pattern strongly depends on the main lobe direction. All these considerations apply in relation to a two-dimensional array.
Although arbitrary order Differential Microphone Array (DMA) based systems with Virtual Microphones steerable in arbitrary directions would be highly desirable for localization purposes, however using known DMAs, doing steering in arbitrary directions with arbitrary order Virtual Microphones characterized by polar patterns with shapes comparable to each other is not possible, so continuous steering is infeasible. Doing steering with identical polar patterns of any order is possible only for a discrete set of directions:                0 degrees and 180 degrees for ULAs; and        angle ψm with 1≦m≦M for UCAs.        